(1) Field of the Invention
The present invention relates generally to threat detection systems. More specifically, the present invention relates to a method for calculating expected maximum sensor performance of a sensor grid for detecting threats when the number of possible threat pathways through the sensor grid is so large that the technique of using all possible pathways to determine the expected maximum probability of detection is impractical.
(2) Description of the Prior Art
Over the past decade, reaction to the terrorism threat has led to increased deployment of threat detection systems at airports and densely populated events as well as accelerated research and development of new threat detection systems. Potential terrorists have a myriad of weapons from which to choose such as knives, handguns, small assault weapons, explosives, dirty bombs, and the like.
In general, particular threat detection systems focus on detecting a specific weapon characteristics. For instance, a munitions or explosives detection sensor would detect trace explosive chemicals while a radiation detection system would detect radioactive material. Unfortunately, no one system will detect every possible weapon. Combining multiple detection sensors to cover a broad spectrum of weapons, however, should greatly improve the overall probability of detecting a weapon on a terrorist.
FIG. 1 illustrates this concept with a multi-layered target detection system having major components 12, 14, and 16 for scanning targets 15 such as pedestrians. Note that the depicted sensors do not represent any particular sensors. The depicted sensors preferably represent a broad range of coverage patterns, automated sensors and man-in-the loop sensors. The first layer 30 comprises long-range tripwire sensor array 12 that detects suspicious targets from among the many targets or pedestrians 15. First layer 30 designates likely threat 24 for tracking and further scrutiny by subsequent layers.
In the second layer 32, the designated likely threat 24 is tracked along threat trajectory 22. Tracking sensors 14 are part of a second layer 32 that further scans threat 24 for biometric, spectral, anomalous, and physical features indicating that threat 24 may be carrying weapons.
All suspicious targets identified by second layer 32 are then passed off to a confirmation layer 34, which either confirms or denies the presence of weapons on the target. Confirmation sensor 16 will determine a confirmed threat 20 using hidden device detection, bulk explosive detection, trace detection, and/or electronics detection. Layer 34 may comprise an operator with computer 18 that is utilized in conjunction with system operation and which receives the sensor data produced by tripwire sensor array 12, tracking sensors 14, and confirmation sensors 16.
This particular deployment scenario makes sense when layer 30 has a scan rate fast enough to scrutinize all of the candidate targets and cull them for subsequent layers with potentially slower scan rates. Selecting the specific fusion rules to combine detection information within and across layers depends on specific sensor scan rates. Culling candidate targets may not be necessary when all sensors have high scan rates.
In 2010, the Naval Surface Warfare Center Panama City Division (NSWC PCD) developed a System Performance and Layered Analysis Tool (SPLAT) that evaluates candidate terrorist threat detection systems. Given a sensor deployment pattern, SPLAT combines sensor performances, scenario data, and pedestrian flow to analytically compute expected system performance in terms of probability of detection (pd) and false alarm (pfa). The analysis divides the detection area into rectangular pixels.
FIG. 2 illustrates this pixelation using five-foot by five-foot pixels referred to herein as voxels 240. Straight line path 230 represents one possible path through detection zone 250. In this example, path 230 starts at a starting voxel in row 1, with starting column Cs. Path 230 ends at the ending voxel, which can be described as being in the last row, at ending column Ce. Because the 2010 pedestrian flow model describes all possible trajectories through the detection area as forward motion only, straight-line paths, SPLAT can enumerate all possible straight -line paths and explicitly determine the pd and pfa along each voxel in the path.
As one example of this type of analysis, shaded pixels or voxels, such as voxels 340, in FIG. 3 illustrate the voxels that the displayed straight-line path 330 of a potential threat crosses. The voxels represent regions in which detectors for threats may be found. SPLAT could be used to determine the probability of detection or likelihood of a false alarm.
Extensive experience with mine-hunting systems has demonstrated that the typical approach of modeling multiple detection opportunities along a trajectory of a target as independent Bernoulli trials tends to be over optimistic. This unrealistically inflates overall probability of detection. For instance, consider a potential threat standing still in a voxel and let a first sensor have a probability of detection for that voxel equal to 0.5. Furthermore, let the entire detection process for the first sensor take two seconds. The first sensor would then have ten detection opportunities if the threat were stationary for twenty seconds. Under the independent Bernoulli trial assumption, the overall probability of detecting a threat at least once over twenty seconds would be 1.0-(0.5)10 which equals 0.999022. As the time the target remains stationary in the voxel increases, the probability of at least one detection would asymptotically approach 1.0. However, this analysis is inherently flawed in that each detection opportunity is not independent from the others.
In general, if a detection model for a sensor were capable of including each and every variable that affected its performance, the outcome of a detection opportunity would not be random at all. Instead, it would be completely deterministic.
In practice, however, we can only capture a subset of all of the variables that affect sensor performance. Furthermore, we cannot measure this subset with absolute precision. Many variable measurements include random noise. Given an imprecise measurement subset, however, we can still measure the performance of a sensor for a random target. Repeating this process over and over is a standard methodology to determine a sensor probability of detection for a truly random target. However, the idea of a random target explicitly means that both the excluded variables and any random noise components on the variable measurements must be truly random in nature.
The analysis in the preceding example failed to capture the point that although the excluded variables were in fact random for the first detection opportunity, they were no longer random for any subsequent detection opportunity. In fact, there was likely very little change in the excluded variables from one detection opportunity to the next since the time interval was only two seconds. Whether or not the random noise on the measured variables is truly random from one detection opportunity to the next depends on the nature of the measurements and how these measurements are taken. Therefore, as a target moves through a layer presenting detection opportunities, many of the variables, both included and excluded, affecting sensor performance are highly correlated. Therefore, these detection opportunities are not independent, but rather highly correlated.
Note that for a detection system comprised of a system -of-systems, measuring individual sensor performances separately fails to capture correlations between the sensors. Properly measuring joint sensor performances requires testing all of the sensors at the same time; this ensures that the environmental test conditions and target scenarios are identical. Unfortunately, in practice, the number and range of sensor variables makes evaluating sensor performance over all possible variable mixture levels virtually impossible.
For each sensor type, SPLAT analysis employs the conservative approach of using the maximum probability of detection along the target trajectory through a detection layer as a single, discrete probability of detection opportunity for the corresponding sensor type. Although this nonlinear approach makes the mathematical analysis extremely complex, this approach does provide an analytic solution without knowing joint sensor probabilities of detection over all detection opportunities. Even though it underestimates probability of detection, it does not over estimate it. It is a conservative and practical solution that accounts for correlated detection opportunities in an environment in which joint sensor performances are unknown.
Because the 2010 SPLAT pedestrian flow model describes all possible trips through the detection area as forward motion only, straight-line paths, SPLAT can enumerate all possible trips and explicitly determine the maximum pd along each trip.
However, instead of a straight-line path, in a more desirable stochastic flow model, pedestrian paths are described as a series of cell-to-cell steps through the detection zone as illustrated by the piece-wise linear path example of FIG. 4. Unfortunately, this stochastic flow modeling has created a combinatorial explosion. There are now too many paths to explicitly enumerate so SPLAT can no longer determine the true maximum pd along each and every path. Addressing this problem, and discussing the above figures and other figures in more detail hereinafter, the present invention provides for a unique expected maximum probability of detection technique, which approximates results obtained by enumerating all possible paths through a detection zone.